Thermal Expansion at a Crystal Surface

Abstract

A lattice-dynamical theory is presented of the thermal expansion of a Bravais crystal slab. The theory incorporates the static temperature-independent relaxation of the inter-planar spacings in the vicinity of the crystal surface, the homogeneous temperature-dependent deformation (thermal expansion) of the crystal arising from cubic anharmonic terms in the crystal potential energy, and temperature-dependent changes in the interplanar spacings at the surface arising from the same source. Numerical estimates of these effects are presented for a nearest- and next-nearest-neighbor central-force model of $\alpha$-iron.